It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum).
Since it only depends on two of the observations, it is most useful in representing the dispersion of small data sets.
The range, T, has the cumulative distribution function[3][4] Gumbel notes that the "beauty of this formula is completely marred by the facts that, in general, we cannot express G(x + t) by G(x), and that the numerical integration is lengthy and tiresome.
We can assume without loss of generality that the support of each Xi is {1,2,3,...,N} where N is a positive integer or infinity.
In particular, the range is a linear function of order statistics, which brings it into the scope of L-estimation.